What do I do when a driver refuses to give me their insurance & vehicle info in IL?

I've found myself to be in a totally awkward situation and am wondering if there's any solution to the problem I'm in. Basically, I was rear ended by a woman Wednesday morning, it was pretty hefty damage to my vehicle to the point where my trunk won't even close. This was on an Illinois interstate (I-90), therefore it is handle by the Illinois State Troopers and the Illinois Tollway system. We both called the police to come out to make a report but we were sitting on the shoulder of the road for 2 hours. I was pretty fed up and frustrated with the situation and told the other driver that we should just go report the accident ourselves. We exchanged contact information and I grabbed her license tag number and the phone number to her insurance agent. At this point in time I had no idea that Chicago police do not handle anything on the tollways and it's all up to State Troopers until I got home and did some research. I finally got through to the number I needed after making numerous calls to police stations in an attempt to make a report. Didn't get to talk to an operator because all lines were busy, but the prompt clearly explained that I needed the other drivers VIN number, Insurance Policy number, Date of Birth, etc. Without this info, I could not file an accident report. No problem I think, I'll just call her up and ask for the necessary information. Of course she doesn't pick up the phone and hasn't called me back, I've been leaving numerous messages and calling her at least 4 times a day. So 1. I can't file a police report without this info, and 2. I can't file a claim against her insurance company with no accident report. It is already Saturday and no word from her. I did manage to get her address, home phone number, and year, make, model and license tag. Is there anything I can do to file an accident report against her even though I lack the necessary info? Also is it to late to do so? I know it was a stupid mistake on my part to not get this information right away, but she seemed trustworthy and felt bad about the situation, and I was in a hurry to get moving off of the highway. Obviously it seems that I'm screwed, and the only thing I can think of is getting a lawyer involved. I have basic coverage so my insurance will not cover any cost to fix my vehicle.